Extract from educational CD-ROM “The Geonauts inquire into the oceans”, OCA/CNES © 2000
Tides:
dancing to the Moon's beat
Tides are amazing things. Every day along the coastline the sea comes in and goes
out, with a difference of several metres between high and low tides. In Antiquity,
people believed that they were caused by the breathing in and out of an enormous
sea monster. It was only in the late 17th century that Newton gave the first
explanations. Just like planets, tides are governed by the law of gravitation. The
reciprocal attraction of the Moon and, to a lesser degree, the Sun causes this
movement in the oceans.
The Moon attracts the whole Earth
The Earth’s mass attracts the Moon, which is why it stays in orbit. Similarly, the
Moon’s mass creates a force which attracts the Earth and oceans, known as the
force of gravity. It is gravity which forces the Earth towards the Moon (the force
is inversely proportional to the square of the distance between the two bodies).
Every single particle of matter in or on the Earth is affected, whether on the
surface or deep down towards the core. However, the nearer the particles are to
the Moon, the more they move.
For example, the point located on the Earth’s
equator nearest the Moon (B) will be more
attracted to the Moon than the diametrically
opposed point (A). In terms of movement
created by the force of gravity, point B will
move three times more than point A. If B moves
30 centimetres, for example, A will only move
10. The centre of the Earth (O) and all the
Diagram showing the Earth’s
points along the axis of the Earth’s poles will
deformation due to the Moon’s
move 20 centimetres nearer the Moon (less than
gravitational attraction.
B but more than A). Point A will therefore be
10 centimetres further from the centre of the Earth (20 cm - 10 cm). Likewise,
point B moves 10 centimetres away from the centre of the Earth (30 cm-20 cm).
This force affects the Earth symmetrically, creating a bulge around the Earth along
the Earth-Moon axis. Remember that the Earth completes a revolution in
approximately 24 hours (23 hours and 56 minutes to be precise). Meanwhile, the
Moon turns around the Earth in the same direction (it completes a revolution of the
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Extract from educational CD-ROM “The Geonauts inquire into the oceans”, OCA/CNES © 2000
Earth in 27.3 days). If you stand at the same point, you will see the Moon rise about
25 hours after the previous moonrise. The time between 2 high tides is half of
25 hours, i.e. 12 hours 30 minutes. At the same time, a tide is high at a particular
point and its antipode but low in the two perpendicular directions.
The Sun joins forces with the Moon
The force of gravity exercised by the Sun, which is what keeps the Moon in orbit
around it, also affects tides. Its force is only half that of the Moon because
although it is 27 million times bigger, its attraction is less because it is 375 times
further away. (This shows how important distance is when calculating the force of
gravity). When the three planets (Earth, Moon and Sun) are aligned, the forces are
combined and the tides are bigger than usual. They are then called spring tides.
When the three planets form a right angle, the forces contradict each other and
the tides are smaller than usual. They are then called neap tides. In the spring and
autumn, when the Sun is along the equatorial plane, its attraction is greatest. That is
when equinox tides occur.
The ocean’s response
The ocean is a fluid. It is a vibrating system subject to periodic excitation. Its
response to the excitation is greater if the period of excitation is near its natural
oscillation period.
To illustrate this phenomenon, let us look at a guitar string. If you pluck a string,
the sound produced has a natural period corresponding to the string’s own
characteristics and its tension. The string will vibrate more if the excitation is near
its natural period. This is due to a physical phenomenon known as resonance. In the
middle of the string there is the vibration “node” where vibrations are strongest.
The vibrations are weakest at both ends, known as the “antinodes”. In the ocean,
the water’s response to the forces of attraction depends on the shape of the ocean
basin in question. In large basins (such as the Atlantic, Pacific or Indian oceans), the
tide can be created and move normally. Near the shore, the water is shallower and
the tidal effect is more pronounced. The shape, size and depth of coastal features
(continental plates, bays, gulfs etc.) given them a natural period. The “nodes”
(strongest vibrations) are found in the middle of ocean basins.
Now let us look at the example of a bowl of water which will symbolise an ocean bay.
If we pick it up and start to walk across the room, we transmit to the water
impulses with a certain period—in this case, the period of our stride. If our strides
match the size of the bowl, the impulses we are sending to the water will be close to
its natural period, so the water will slop out. If, on the other hand, we take shorter
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Extract from educational CD-ROM “The Geonauts inquire into the oceans”, OCA/CNES © 2000
strides then the water’s movement will be smaller. In the case of the ocean, if the
period is the same as the tidal period, the tides are bigger (think of a swing—when
you want to push somebody to make them go even higher, you wait until they have
reached their highest point before pushing as this amplifies the movement).
The difference in sea height between a high tide and a low tide is called the tidal
range. In the middle of the oceans, the difference is around 1 metre. Nearer the
coastline, however, it can be greater because the shallowness of the water and the
extent of the continental plates emphasise the tide. At Mont Saint-Michel in
France, the tidal range is around 15 metres. The biggest tidal range though is in the
Bay of Fundy north of Boston, United States. There it reaches 20 metres!. In the
Mediterranean sea, on the other hand, the tidal range is minimal (around 20
centimetres). This is because the basin is narrow and deep so the water cannot
respond as much. Altimetry satellites such as TOPEX/Poseidon and recently
developed models have pinpointed the amplitude of tides in the middle of oceans to
within 2 centimetres.
Map showing tidal ranges (credits: GRGS/LEGOS/CNES, Toulouse)
Earth tides
You may be surprised to learn that tides also exist on Earth. The Moon and Sun’s
mass creates a force which deforms not only the oceans, but also the land. The solid
Earth actually changes shape. This deformation is mainly elastic in nature and
creates geometric distortions of the Earth’s surface. Every day, under the effect
of Earth tides, houses in a given area rise and fall by 20 to 30 centimetres. You
cannot see this happening because all the houses for hundreds of kilometres around
move at the same time and in exactly the same way.
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Extract from educational CD-ROM “The Geonauts inquire into the oceans”, OCA/CNES © 2000
The gradual separation of Earth and Moon
The Moon orbits around the Earth under the effect of gravitation.
What is more, subject to powerful tidal forces by the Earth, the Moon
turns around on its own axis at the same speed and in the same
direction as its revolution around the Earth. This is why we always see
the same side of the Moon. Like the Moon’s influence on the Earth, the
Earth’s tidal forces on the Moon cause movements in its soil.
Under the influence of the Moon’s tidal effect on the Earth, our
planet is turning around more slowly over time: the length of one day
grows by 0,00164 seconds every century. This is only a slight slowing
down, but it is regular. It is thought to have two main causes. One is
the dissipation of energy caused by friction during tidal movements, especially in
shallow seas, and the other is the action of the equatorial bulge created by tidal
forces, as this bulge intensifies the Earth’s tidal force on the Moon. The
combination of these two phenomena are causing the Moon to revolve faster. This
means that Earth, which is a satellite of the Moon, is gradually moving away from its
mother planet. It moves about two metres away every century.
Bibliography
Satellite Altimetry and Earth Sciences, a handbook of techniques and applications,
edited by Lee-Lueng Fu and Anny Cazenave, International Geophysics Series,
Volume 69, 2001.
BT (Bibliothèque de Travail): Les marées côtières, Editions PEMF, no. 1047, April
1993.
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